
where \(\rho _{\rm in}\)  and \(\rho _{\rm out}\)  is the total energy density inside and outside the Hubble volume, respectively.
When the energy density contrast \(\delta \)  exceeds the critical value \(\delta _{c} = 0.45\)  [1]}, [2]}, the inside of the Hubble volume can gravitationally collapse into a PBH.
Therefore, the mass of PBHs is roughly determined by the Hubble horizon mass at the time when the PBHs are produced.
For the EWPT, the mass of PBHs is about \(10^{-5} M_{\odot }\)  (\(M_{\odot }\)  is the solar mass).
Thus, the fraction of the PBHs \(f_{\rm PBH}\)  produced from the first-order EWPT can be probed by the current and future microlensing observations such as Subaru HSC, OGLE, PRIME and Roman Space Telescope.
The fraction \(f_{\rm PBH}\)  can be determined by the phase transition parameters \(\alpha \)  and \(\beta /H\)  in Eqs. (REF ) and (REF ).
The method of calculating the fraction \(f_{\rm PBH}\)  is explained in the Appendix.
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